This problem occurs in Word 2007 when using equation editor.
Occasionally I will be working on a document containing lots of equations made in equation editor. I decide to save and an error saying "A file error has occured" appears, and the document refuses to save.
This is a very widespread problem. A quick Google search brings up many unresolved threads on different forums, all concerning this issue. e.g.:
The following previously suggested "solutions" do not work:- Cutting and pasting the formulas into a new document
- Accepting all changes to document in the review tab
- Using 'open and repair'
- Systematically cutting formulas away and trying to save, in order to find out which formula is causing the problem. (I don't know why this won't work for me)